HG 1628 
.K7 
Copy 1 






j LIB RARY ^OF CONGRE SS. 



! UNITED STATES OP AMERICA. 



. 



MPLS 



TIBlSf. 



L 




Simple Interest 

TEEATISE: 



IN WHICH THE LATEST MODERN IM- 
PROVEMENTS, AND SUCH OLDER PRINCI- 
PLES AS HAVE BEEN WELL ESTABLISHED 
BY PRACTICAL TESTS, ARE HARMONIZED 
TOGETHER, BY INTRODUCING THE 

NEW AND VALUABLE METHOD 

DEVELOPED BY THE AUTHOR, AND 
A COMPACT SYSTEM OF USE- 
FUL INTEREST TABLES. 

DESIGNED AS A COMPLETE TEXT-BOOK 
ON THE SUBJECT FOR THE 

SCHOOL AND BUSINESS OFFICE, 



B> 

WILLIE H. KNOWLTON. 



Published By The 
MESSENGER COMPANY, 

VICTORY, CAYUGA CO., N. Y. 

1875. 



3 f mmjut ^ 



H F/. 



Entered according to act of Congress, in 
the yei^r 1875, fo/ Willie H. Knowlton, in 
the office of the Librarian of Congress, at 
Washington. 



As the finding of interest, on a certain 
sum of money, for a given rate and time, 
forms the principal portion of several im- 
portant rules of percentage, it is of the 
utmost importance that the method used 
should not only be well understood, but 
based on as concise principles as can be 
used with accuracy, in their application 
to practical examples in the schoolroom 
or business office. 

Every one who has had occasion to 
solve examples in interest is well aware 
of the perplexity and discouragement 
that often attend the methods commonly 
pursued. For example, the operation 
may, during necessary divisions, contain 
decimals, which are carried out as far as 
may be deemed efficient, and the remain 
ing ones disregarded. If the division is 
perfect, the answer may be found with 
accuracy ; and in proportion to the deci- 
mals used will the approach to correct- 
ness be developed. When ihe principal 



4 SIMPLE INTEREST. 

is a small sum, or the time of short dura- 
tion, the result may be sufficiently exact 
for ordinary purposes where only four or 
^ve places of decimals are employed ; but 
where the principal is large, or the time 
of long duration, the deviation of the 
final result from the true answer will be 
very marked, unless a tedious number of 
decimal figures are used. This is not 
necessarily taken into account in approxi- 
mate transactions, though a rule which 
is exact, provided it is cot too compre- 
hensive, is to be admired and chosen. 
But the scholar and teacher find it neces- 
sary that the rule employed in interest be 
capable of bringing about perfect results ; 
and then, of course, the more simple and 
brief this can be made, the better will the 
accountant be satisfied. There are meth- 
ods described in the principal Arithmetics 
used in American schools that are accu- 
rate when rightly applied, but are not 
sufficiently so as understood by many op- 
erators. When the examples are worked 
decimally, and the divisions are not per- 
fect, as is often the case, the operator 
may use the utmost care to avoid mis- 
takes, and yet fail to find the correct an- 
swer—for the reason that unknown deci- 
mal parts have been removed- 



SIMPLE INTEREST. 5 

To present in one harmonious whole 
the latest improvements in the subject of 
simple interest, by introducing what is be- 
lieved to be the best and most complete 
interest method yet developed, and finally 
to give the professional or business man, 
in a compact and convenient form, a 
most valuable and reliable system of in- 
terest tables, is the design of this work. 
No pains have been spared to present it 
in a scientific and attractive manner, and 
at the same time to make it thorough and 
accurate. 

Should this minature volume receive 
the kindly notice of educators and bus- 
iness persons, and perchance be the 
means of relieving the embarrassment of 
some weary student, the author's highest 
hopes will have been attained. 

VICTORY, OCTOBER, 1875. 



B!TTK@PiGT!)@fil). 



Modern rules for computing interest 
are based upon the principle that every 
interest month contains 30 days, and ev- 
ery interest year 12 months. This gives 
860 interest days for each year, instead of 
365 days for a common year, and 866 
days for each leap year. As interest is 
reconed at a certain per cent, per annum 
on the sum lent, it is evident that this 
principle involves a slight inaccuracy of 
one seventy-third. But this using 30 inte- 
rest days for a month, seems to have been 
early adopted for its convenience, and is 
universally chosen as the standard among 
professional and business persons every- 
where. 

The New Method, developed and first 
published in this work, depends much on 
the aid of cancellation for its briefness 
and utility. The method may be used to 
very good advantage without cancelling 
equal factors ; but as this nearly always 
can be accomplished, and very much les- 
sens the labor of multiplying the exam- 
ples in interest, it has been introduced in 
the following pages. 



Simple Interest. 

In business transactions people find the 
necessity of claiming a certain portion of 
money for the use or profit of cash loan- 
ed, or its equivalent. When money is 
loaned by an individual or firm, the law 
provides that such persons shall receive a 
certain per cent, yearly on the sum lent. 
Thus, if A loans B money at 6 per cent., 
for one year, A will be entitled to 6 per 
cent, of the sum lent ; if for two years* 
he will be entitled to 6 per cent, of this 
sum for each year, and in like proportion 
for any time and per cent. Such a per 
cent, of any sum loaned, which is due the 
lender and payable by the borrower, is 
called interest. Then, 

INTEREST is the sum paid for the 
use of money, or its equivalent. When 
interest is paid on a loan or credit during 
the whole time, and not including inter- 
est previously accumulated, it is known 
as simple interest. Then, 

SIMPLE INTEREST is the sum paid 
for the use of money only, during the 
whole time of the loan. 



8 SIMPLE 1NTEBEST. 

When interest is received on a sum pre- 
viously loaned, the lender is entitled to 
both the loan and the interest. Then, 

AMOUKT is the sum of the loan and 
interest. 

From the above the mind easily percei- 
ves that, in tracing the principles of in- 
terest, there are five parts involved : 

I. The Principal, or the sum loaned. 

II. The Rate, or the per cent, paid per 
annum. 

III. The Time, or duration of the loan. 

IV. The Interest, or the sum paid. 

Y. The Amount, or sum of the princi- 
pal and interest. 

As the term per annum is a Latin 
phrase, signifying by the year, and as in- 
terest is always computed by the year, it 
is understood and omitted in commercial 
forms. 

The rate per cent, is such a part of one 
dollar or one hundred cents, for each 
year, as it indicates. Thus, if one dollar 
is loaned for one year, at seven per cent,, 
1.00 will be the principal ; 7 per cent, of 
this, or seven one hundredths , the rate ; 
1 year the time ; 7 cents the interest ; and 
1.07 the amount. 

Thus it will be seen that the principal, 



SIMPLE INTEREST. :9 

rate, or tinfe, may be variable, while the 
interest or amount is always formed from 
these. The principal and time are each 
in accordance with the arrangement made 
by the parties concerned in a business 
transaction ; while legal interest, or the 
rate established by law varies in different 
states as follows : 



Alabama 

Florida 

Mississippi 

Texas 

New York 

Michigan 

Iowa 

Wisconsin 

South Carolina 

Georgia . + 

Maine 

New Hampshire 

Vermont 

Massachusetts 

Ehode Island 

Connecticut 

New Jersey 

Delaware 

Pennsylvania 

Maryland 

Virginia 



8 per cent 

8 



7 
7 
7 
7 
7 
7 
6 
6 
6 
6 



J 



10 SIMPLE INTEREST. 

North Carolina . . ti per cent. 

Tennessee , . . . 

Missouri ... 6 

Kentucky ... 6 

Indiana ... 6 

Illinois .... 6 

Ohio .... 6 

District of Columbia . 6 

Louisiana ... 5 

The interest on United States* debts 
varies from the states, being established 
by law at 6 per cent. 

The legal rate of interest for England 
and France is each 5 per cent., and of 
Canada, 6 per cent. In some of the Euro- 
pean countries it has been from 20 to 30 
per cent. 

When the rate per cent.* is not mention- 
ed in business transactions, the legal rate, 
of the state wherein the parties agree, is 
always understood. 

On agreement, any rate less than the le- 
gal rate becomes lawful ; but as the legal 
rate in each respective state or country 
is considered to be justifiable to both 
borrower and lender, it is almost univer- 
sally adopted. 

Owing to commercial embarrassments, 
and other causes, parties often give a 



SIMPLE INTEREST. 11 

higher rate of interest than that establish- 
ed by law. Such is called usury or illegal 
interest. For the same reason, a certain 
sum is often given, and not reckoned at 
any rate per cent. This is called carrying 
or sham money ; although it is virtually 
the same as usury. 

In modern financial and commercial 
business the term per cent, is generally 
expressed by^ the charact er %. Thus, 7 
per cent, may be written 7 %. 



knowlton's 
INTEREST METHOD, 

FOR COMPUTING THE INTEREST OP ANY 
SUM, FOR A SPECIFIED TIME, AT ANY RATE 

PER CENT. 



When The Time Contains Years. 



1. Find the interest of 13 dollars, for 5 
years, at 5 %. 

OPERATION. 

— X A X - = $3.25, Ans. 
100 1 1 

Analysis. Knowing the interest of one 
dollar, for one year, at 5 %, to be 5 cents, 



12 SIMPLE INTEREST. 

it must be five one hundredth dollars, 
when reduced to a fraction. Now, since 
five one hundredth dollars is the interest of 
one dollar, for one year, at 5 %, 5 times 
this will be the interest of one dollar, for 
the number of years, at 5 % ; and 13 times 
this will be the interest of the whole 
number of dollars, for the number of 
years, at 5 %, Indicating the operation, 
and multiplying by the aid of cancella- 
tion, gives $3.25,' the required answer. 



When The Time Contains Years And 
Months. 



2. What is the interest of $25, for 2 
years and 4 months, at 6 % ? 

OPERATION. 

-A. xlx 2 -- $3.50, Ans. 
100 3 1 ~ 

Analysis, Since the interest of one 
dollar, for one year, at 6 %', is 6 cents, it 
must be six one hundredth dollars represent 
ed fractionally. As there are months in- 
cluded in the time, the years and months 
should be reduced to years and fractions, 
giving two and one third ; and this reduc- 



SIMPLE INTEREST. 13 

ed to an improper fraction, gives seven 
thirds . If six one hundredth dollars is the 
interest of one dollar, for one year, at 6 #, 
seven third times this will be the interest 
of one dollar, for the number of years, at 
6 % ; and 25 times this will be the interest 
on the whole number of dollars, for the 
number of years, at 6 %. Indicating the 
operation, and multiplying by the aid of 
cancellation, gives $3.50, the required re- 
sult, 



When The Time Contains Years, 
Months And Days. 



3. What is the interest of $400, for 1 
year 5 months and 13 days, at 7 % ? 



OPERATION. 



X ^- —$40,67 7-9, Am. 



7 x 523 

100 360 ~ 1 

Analysis. As the interest of one dol- 
lar, for one year, at 7 #, is 7 cents, it 
must be seven one hundredth dollars, 
when represented fractionally. Since 
there are days included in the time, the 
years, months, and days, should be re- 
duced to days, which gives 523 ; and as 



14 SIMPLE INTEREST. 

there are 360 interest days in a year, 523 
days must be equal to five hundred twen- 
ty-three three hundred sixtieth } ears. Then 
if seven one hundredth dollars is the int. 
of one dollar, for one year, at 7 %, five 
hundred twenty-three three hund. sixtieth 
times this will be the interest of one dol- 
lar, for the number of years, at 7 % ; and 
400 times this will be the interest on the 
whole number of dollars, for the number 
Of years, at 7 %. Indicating the operation, 
and multiplying by the aid of cancella- 
tion, gives $40.67 7-9, the result required. 

If the student has carefully learned the 
preceding truths, operations, and analy- 
ses, he will be quite prepared to treasure 
Up the following 

RULE FOR OPERATION. 

Indicate the rate of interest as so many 
one hundredth dollars, by placing it over 
the number 100. Find the whole number 
of years, by reducing years and months 
to yeaisand fractions, and years, months, 
and days, to days— -calling them so many 
three hundred sixtieth years, by writing 
them over the number 360. Change the 
number of dollars to a fraction. Indicate 
the operation, by writing the rate value, 



SIMPLE INTEREST. 15 

the number of years, and the whole num- 
ber of dollars, separated by the sign of 
multiplication, finishing by cancellation 
whenever practicable. 

EXAMPLES FOR PRACTICE. 

4 Required the interest of $240, for 
4 years 2 months and 5 days, at 6 per 
cent. 

OPERATION. 

5. What is the interest of $ 14.10, for 
6 months and 10 days, at 5 % ? 

Ans. .3721-12. 

6. What is the interest of $3500, for 
60 days, at 7 % ? 

Ans. $40,831-3. 

7. Find the Interest of one dollar, for 
1 year 5 months and 28 days, at 93-5 
per cent. 

OPERATION. 

9 1 = 48. 48^ 100 _ J2_ _ the 

5 5 ' 5 • — 125 ~" 

rate value. Ans. .14342-3. 



16 SUPPLE INTEREST. 

|3g*In the preceding example the rate is 
divided by 100, which is the same as plac- 
ing it over that number. The latter form 
would give a complex fraction. 

8. What is the interest of $722, for 16 
days, at 6 % ? 

9. What is the amount of $1000, for 1 
year i month and 1 day, at 6 % ? 

Ans. $1065,1662-3. 

10. What is the interest of 54 dollars, 
for 20 days, at 1 % ? 

Ans. three one hundredth dollars, or 
3 cents. 

11. What is the interest of $80, for 7 
years and 7 months, at 5 % ? 

12. What is the amount of 1 dollar, for 

9 months and 10 days, at 7 % ? 

Ans. 1.054-9. 

13. What is the interest of $15, for 8 

months, at 62-3$ ? 

Ans. .662 3. 

14. Required the interest of $200, for 

10 months and 20 days, at 7 per cent. 

Ans. $12,444-9. 

15. Required the interest of $100, 

from March 8 to August 25, at 6 %. 

Ans, $2.83+-. 



SIMPLE IHTEREST. 17 

16. A note of 315 dollars, dated No- 
vember 6, 1873, became due December 
SO, the following month ; what was the 
interest at 7 % ? 



$600 

Syracuse, Feb. 10, 1874. 
17. Six months after date, I promise 
to pay J. Ross, or order, 600 dollars, for 
value received. 

Stephen Briggs. 

This note was settled Jan, 23, 1875 ; 
How much was then due, no payment 
having been made ? 

Ans. $640.0164-. 



IS 



SIMPLE INTEREST. 



USEFUL INTEREST TABLES. 



FORMED BY MEANS OF KNOWLTON's 
INTEREST METHOD, FOR THE USE OF BUS- 
INESS AND PROFESSIONAL PERSONS EVERY- 
WHERE. 



TABLE NO. I. 



Giving the interest of one dollar, for 
any number of years from one to ten, at 
5, 6, 7, and 8 per cent. 



at a®* 


5 % 


6 % 


7 % 


8 % 


For 1 year 


.05 


.06 


.07 


.08 




' 2 " 


.lo 


.12 


.14 


.16 




1 3 " 


.15 


.18 


.21 


.24 




i 4 « 


.2o 


.24 


.28 


.32 




i 5 « 


.25 


.3o 


.35 


.4o 




< 6 " 


.3o 


.36 


.42 


.48 




4 7 " 


.35 


.42 


.49 


.56 




4 8 " 


.4o 


.48 


.56 


.64 




< 9 « 


.45 


.54 


.63 


.72 




1 10 " 


.5o 


.60 


.7o 


.80 



The above table gives the interest of 
one dollar, for any number of years under 
ten. Should any number of years higher 
than ten be desired, the interest may eas- 
ily be found by multiplying the rate by 
the number of years. 



SIMPLE INTEREST, 



19 



TABLE NO. II. 



Giving the interest of one dollar, for 
any number of months in a year, at 5, 
6, 7, and 8 per cent. 



AT f&~ 


i 5 # 


6 % 


7 % 


8 % 


For 1 mo. 


.oo41 


.oo5o 


.oo58 


.0066 




. 2 " 


.oo83 


.oloo 


.0II6 


.0133 




c 3 „ 


.0125 


.ol5o 


.ol75 


.o2oo 




< 4 « 


.0166 


.o2oo 


.0233 


.0266 




< 5 « 


.o2o8 


.o25o 


.0291 


.c333 




< 6 " 


.o25o 


.odoo 


.o35o 


.o4oo 




14 7 " 


.0291 


.o35o 


.o4o8 


.0466 




" 8 " 


.0333 


,o4oo 


.0466 


.0533 




" 9 " 


.0375 


.o45o 


.0525 


.0600 




u 10 " 


.0416 


.o5oo 


.0583 


.0666 




u n « 


.0458 


.o55o i .0641 


.0733 




1 12 " 


.o5oo 


.0600 


.o7oo 


.0800 



Table number two and three gives the 
interest for months and days, true to four 
decimal places. Many of the numbers 
are exaci, and all are so slightly approxi- 
mate that they may freely be used for 
business purposes everywhere. 



TABLE NO. III. 



Giving the interest of one dollar, for 
any number of days in a month, at 5, 6, 



"20 SIMPLE INTEREST. 

7, and 8 per cent. 



AT HT 


5 % 


6 % 


1 % \ § % 


For 1 


day 


.oool 


.ooo1 


.oool 


.ooo2 




" 2 


n 


c ooo2 


.ooo3 


.ooo3 


.ooo4 




11 3 


u 


.ooo4 


.ooo5 


.ooo5 


.0006 




" 4 


i< 


.ooo5 


.0006 


.ooo7 


.0008 




u 5 


a 


.0006 


.0008 


.ooo9 


.ooll 




" 6 


a 


.0008 


.oolo 


.ooll 


.ool3 




u 7 


a 


.ooo9 


.ooll 


.ool3 


.ool5 




4 8 


a 


.ooll 


.ool3 


.ool5 


.ool7 




" 9 


a 


,ool2 


.ool5 


.ool7 


.oo2o 




14 lo 


a 


.ool3 


.00I6 


.nol9 


.oo22 




" 11 


u 


.ool5 


.00I8 


.oo21 


.oo24 




14 12 


a 


.00I6 


,oo2o 


.oo25 


.oo26 




" 13 


a 


.00I8 


.oo21 


.oo25 


.oo28 




4 14 


i' 


.ool9 


.oo23 


.oo27 


.oo3i 




4 15 


a 


.oo2o 


.oo25 


.oo29 


.oo33 




4 1« 


n 


.oo22 


.oo26 


.oo31 


.00b 5 




4 17 


i i 


.oo23 


.oo28 


.oo33 


.oo37 




4 18 


a 


.oo25 


.oo3o 


.oo35 


.0040 




4 19 


n 


.oo26 


.oo31 


. oo36 


.oo42 




4 2o 


a 


.oo27 


t oo33 


.oo33 


.oo44 




4 21 


a 


.oo29 


.oo35 


.oo4o 


.oo46 




4 22 


u 


.oo3o 


.oo36 


.oo42 


.oo48 




4 23 


a 


,oo31 


.oo38 


.oo44 


.oool 




4 24 


u 


.oo33 


.oo4o 


.oo46 


.oo53 




4 25 


(i 


.oo34 


.oo41 


.oo48 


.oo55 




4 26 


<t 


.oo36 


,oo43 


.oo5o 


.000? 




4 27 


it 


.oo37 


.oo45 


.oo52 


.0060 




4 28 


<< 


.oo38 


.oo46 


.oo54 


.ooo2 




4 *9 


<< 


.oo4o 


.oo48 


.oo56 


.oo64 




4 So- 


t< 


.oo41 


. 0000 


.0068 


.0066 



SIMPLE INTEREST. 21 

To use the preceding interest tables, 
glance down the vertical column of fig- 
ures, under the given per cent, to the 
number opposite the given time in the 
first column of each table. The sum of 
these numbers will give the interest of 
one dollar, for the whole time, at the giv- 
en rate per cent ; and this multiplied by 
the principal, will give the required ans- 
wer. Thus, 

18. Required the interest of $32o, for 
2 years 1 month and 5 days, at 7 %. 

OPERATION. 

Glance down the vertical column un- 
der 7 #, in the required tables, and find 



Interest for 2 years 


.14oo 


" " i month 


.oo58 


" 5 days 


.ooo9 



Sum 1467 

and, .1467 X 32o zz 46.94, Ans. 



j 



22 



SIMPLE INTEREST. 



CONTENTS. 




Preface 


. 3 


Introduction 


. 6 


Simple Interest . 


. . 7 


Legal Interest Rates . 


. 9 


Knowlton's Interest Method 


. . 11 


Rule For Operation . 


. 14 


Examples For Practice 


■ . 15 


Useful Interest Tables 


• . 18 



